The ZEC said it had not seen any evidence of rigging or cheating. International observers said they had seen few problems other than some poor organisation in places.

The first results from the election – which will determine the former British colony’s future for decades – are due from 3pm (1300 GMT) on Tuesday, the ZEC said, with final results due by 4 August.

The election pitted Chamisa, 40, a lawyer and pastor whose only experience of power was a stint as a minister in a coalition government several years ago, against Emmerson Mnangagwa, 75, a longtime Mugabe aide and head of the ruling Zanu-PF party. The two represent dramatically different ideologies and political styles, as well as generations.

Chamisa said in a 5am tweet that the Movement for Democratic Change had “done exceedingly well”, according to results from a majority of polling stations.

There was no confirmation of his claim. However, results from each of 10,985 polling stations are posted in public by officials. Several civil society groups are collating these, though they are not allowed to release full results before the official tally is known.

One thing Chamisa has done is to re-energise voters. He had to end voter apathy. He did that. After Chamisa took over, we saw the number of people registering to vote going up. Especially the young people. Those who had lost interest in voting. He made them believe again. #POVpic.twitter.com/52afqRxJbF

Activists said the results were still too close to call but the general trend appeared to be in the opposition’s favour. Mnangagwa tweeted that he was “delighted by the high turnout and citizen engagement so far”.

He added: “The information from our reps on the ground is extremely positive! Waiting patiently for official results as per the constitution.”

Pre-election opinion polls gave Mnangagwa, a dour former spy chief known as “the Crocodile” for his reputation for ruthless cunning, a slim lead over Chamisa, a brilliant if sometimes wayward orator.

Early polling station results seen by the Guardian showed Chamisa winning by wide margins in urban strongholds and in parts of the strongly anti-government south-west.

Support for Zanu-PF historically has been deepest in rural areas, particularly the party’s Mashonaland heartland, where more than two-thirds of Zimbabwe’s 17 million people live. People in the remote north-east appear to have voted by a wide margin for the government.

Chamisa’s claims of imminent victory are consistent with a strategy over several weeks that has sought to put Zanu-PF on the defensive and make rigging more difficult.

If no candidate wins more than half the votes, there will be a runoff in five weeks, though analysts believe this scenario is unlikely. In 2008, dozens of people were killed before a runoff between Mugabe and the MDC’s founder, Morgan Tsvangirai, who died from cancer in February.

Another possibility is negotiations to form a coalition government if the result is very close.

Although the campaign has been free of the systematic violence that marred previous polls, the MDC has repeatedly claimed it has been hindered by a flawed electoral roll, ballot paper malpractice, voter intimidation, bias in the electoral commission and handouts to voters from the ruling party.

There are widespread fears among opposition activists and supporters that the government or the military will refuse to cede power if defeated. This would provoke massive protests, MDC loyalists have said. “If we are robbed, we will go to the streets,” said one MDC supporter, who did not want to be named.

Zimbabwe’s rulers know that a fraudulent election would block the country’s reintegration into the international community and deny it the huge bailout package needed to avoid economic meltdown.

Almost four decades of rule by Mugabe has left Zimbabwe with a shattered economy, soaring unemployment and crumbling infrastructure. Mnangagwa has stressed foreign investment and “unity” during campaigning.

For the first time since Zimbabwe gained independence in 1980 after a brutal guerrilla war against a white supremacist regime, Mugabe was not on the ballot paper. On Sunday the former president said he would not vote for his former party, Zanu-PF, or the current president, and endorsed Chamisa.